We report Chandra observations of GW170817, the first neutron star-neutron star merger discovered by the joint LIGO-Virgo Collaboration, and the first direct detection of gravitational radiation associated with an electromagnetic counterpart, Fermi short gamma-ray burst GRB 170817A. The event occurred on 2017 August 17 and subsequent observations identified an optical counterpart, SSS17a, coincident with NGC 4993 (~10 arcsec separation). Early Chandra (Delta t ~ 2 days) and Swift (Delta t ~ 1-3 days) observations yielded non-detections at the optical position, but ~9 days post-trigger Chandra monitoring revealed an X-ray point source coincident with SSS17a. We present two deep Chandra observations totaling ~95 ks, collected on 2017 September 01-02 (Delta t ~ 15-16 days). We detect X-ray emission from SSS17a with L_{0.3-10 keV} = 2.6^{+0.5}_{-0.4} x 10^38 ergs, and a power law spectrum of Gamma = 2.4 +/- 0.8. We find that the X-ray light curve from a binary NS coalescence associated with this source is consistent with the afterglow from an off-axis short gamma-ray burst, with a jet angled >~23 deg from the line of sight. This event marks both the first electromagnetic counterpart to a LIGO-Virgo gravitational-wave source and the first identification of an off-axis short GRB. We also confirm extended X-ray emission from NGC 4993 (L_{0.3-10 keV} ~ 9 x 10^38 ergs) consistent with its E/S0 galaxy classification, and report two new Chandra point sources in this field, CXOU J130948 and CXOU J130946.
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